Joint signal-to-signal beat interference mitigation for the field recovery of symmetric carrier-assisted differential detection with low carrier-to-signal power ratio.

As a combination of direct detection and coherent detection technologies, self-coherent detection has the advantages of low cost and optical field recovery ability. However, most of the self-coherent detection techniques are limited to single sideband (SSB) signals. Recently, carrier-assisted differential detection (CADD) has been proposed to realize complex-valued double sideband (DSB) signals, but it requires a high carrier-to-signal power ratio (CSPR) to mitigate the signal-to-signal beat interference (SSBI). Later, a more cost-effective symmetric CADD (S-CADD) has been proposed while the required CSPR is still high. In order to alleviate the high requirements of CSPR, we propose a scheme based on the joint of digital pre-distortion (DPD) at transmitter and clipping at receiver to further improve the S-CADD system performance. This joint processing can not only solve the problem of non-uniform distribution of subcarrier signal-to-noise ratio (SNR) caused by non-ideal transfer function, but also the error propagation problem caused by enhanced SSBI under low CSPR. After the validation of the 64 Gbaud 16-ary quadrature amplitude modulation (16-QAM) orthogonal frequency division multiplexing (OFDM) signal transmitted over 80 km standard single mode fiber (SSMF), the CSPR required by the proposed scheme to reach the 20% soft decision-forward error correction (SD-FEC) and 7% hard decision-forward error correction (HD-FEC) can be reduced by 1.3 dB and 2.8 dB, respectively, with a comparison of the conventional S-CADD. The results show the potential of the proposed scheme in the short-reach optical transmissions.

Non-sweep DC component estimation method for a virtual-carrier assisted Kramers-Kronig receiver.

The Kramers-Kronig (KK) receiver has attracted much attention in short-range optical interconnection because of its ability to recover the phase of the signal from the intensity information through KK algorithm. In high-speed KK systems, such as virtual-carrier (VC) assisted ones, an alternating current (AC) coupled photo-detector (PD) is preferred due to relaxing the requirements of analog-to-digital converter (ADC) and electronic amplifier by filtering direct current (DC) component. However, the loss of the DC component will cause the KK algorithm to break down, so it is necessary to accurately recover DC value in the digital domain with multiple-sweep. In this paper, we propose what we believe is a novel non-sweep DC component estimation scheme based on optimized digital carrier-to-signal power ratio (OD-CSPR) method, which can accurately estimate the DC component with only 3-4 iterations in the scenario of VC-assisted KK receiver optical transmission. The scheme utilizes the one-dimensional search optimization algorithm based on golden section search and parabolic interpolation without sweeping. The simulation and experimental results of the proposed non-sweep OD-CSPR method show that the DC component can be estimated accurately in a large CSPR range, and the system performance is close to that of the conventional DC-sweep method. Compared with the typical defined digital CSPR (DD-CSPR) based optimization method, the proposed one can realize optical signal-to-noise ratio (OSNR) gains of 0.9 dB in the back-to-back (B2B) and 0.7 dB under 80 km fiber transmission scenarios respectively with a total bit rate of 160Gb/s.

Blind frequency offset estimation method based on a minimum phase correction error for a full spectrum modulated NFDM system.

To improve the spectral efficiency of a full spectrum modulated nonlinear frequency division multiplexing (FS-NFDM) system, a blind frequency offset estimation (FOE) method has been proposed. The approach based on the minimum phase correction error can achieve high estimation accuracy of sub-MHz without need of any training symbols. Furthermore, in order to reduce the computational complexity, an eigenvalue-shift method is used to get a coarse search interval of FO, and then the one-dimensional optimization algorithm based on golden section search and parabolic interpolation is used to get the optimal FOE for the coarse search interval. The feasibility and reliability of the proposed blind FOE approach have been demonstrated in both BTB and fiber transmission scenarios. Compared with the grid search method, the proposed solving scheme can save hundreds of times of the searches. The experimental results reveal that the proposed method is robust to the amplified spontaneous emission noise and phase noise and has the capabilities of a wide FOE range and a high FOE accuracy.

Multiple-signal-joint-processing-based guard interval shortening method for a CS-NFDM system.

Aiming to further improve the spectral efficiency (SE) of a continuous spectrum modulated nonlinear frequency division multiplexing (CS-NFDM) system, we propose a novel ,to the best of our knowledge, multiple-signal-joint-processing (MSJP)-based guard interval (GI) shortening method. In this method, multiple NFDM time-domain signals are jointly processed as a whole to carry out nonlinear Fourier transform and inverse nonlinear Fourier transform (NFT-INFT) operations. These operations can fuse the multiple NFDM time-domain signals together, which is equivalent to the corresponding inverse process of a fiber transmission. Experimental results show that the normalized SE of the proposed method can reach 0.99 when approaching the limit value of 1 and obtain a 2.33 dB Q2-factor improvement compared with the pre-dispersion compensation (PDC) method under the same GI of 0.03 ns in an 80 km SSMF transmission of a 46 GHz signal bandwidth. Furthermore, in comparison with the PDC method, the proposed method can achieve 32.86% normalized SE improvement in the 1120 km SSMF transmission of 32 GHz signal bandwidth under the SD-FEC of 2.4E-2.

Experimental demonstration of optical waveform transmission with multiple-eigenvalue 16-APSK modulation.

The multi-eigenvalue multiplexing-based discrete spectrum-modulated nonlinear frequency-division multiplexing (DS-NFDM) system with higher-order modulation format has been demonstrated experimentally. After designing the coefficients of the eigenvalue set and the constellation point distribution of 16-amplitude phase shift keying (16-APSK), the realizations of 14-, 30-, and 46-eigenvalue multiplexed DS-NFDM signals have been implemented. The results show that 46-eigenvalue and 30-eigenvalue multiplexed DS-NFDM signals can transmit 50 km and 400 km over a nonzero dispersion-shifted fiber (NZDSF) under soft-decision forward error correction (SD-FEC) threshold of 2.4E-2, respectively. This demonstration shows for the first time, to the best of our knowledge, the record for multiplexed eigenvalue number and data rate of the multiple-eigenvalue-based DS-NFDM system.

Single wavelength MDM-PDM 800-Gb/s net data rate transmission over a standard multimode fiber employing a Kramers-Kronig receiver.

We propose a high-speed multimode fiber short-reach optical interconnect system based on a Kramers-Kronig (KK) field reconstruction with the mode division multiplexing (MDM) and polarization division multiplexing (PDM) technology. In this work, the LP01, LP21a, LP21b, and LP02 modes are selected as independent channels to carry information. The demonstration achieved the 800 Gb/s net data rate per wavelength with a bit-rate-distance-product (BDP) of 8 Tb/s·km. To the best of our knowledge, this is the highest experimental record of a single wavelength BDP over the SMMF with KK detection. In addition, we discuss the system performance after all multiple-input multiple-output (MIMO) and partial MIMO processing and give guidance on the trade-off between system performance and computational resource.

Frequency offset estimation for nonlinear frequency division multiplexing with continuous spectrum modulation.

Carrier frequency offset (CFO) estimation is very important for the optical fiber communications and has been studied widely in linear coherent systems, while only a few works have been reported for nonlinear Fourier transform (NFT) based systems. In continuous spectrum (CS) modulation nonlinear frequency division multiplexing (CS-NFDM) systems, frequency offset (FO) has a great influence on its performance, requiring an improved frequency offset estimation (FOE) method. We found that the oversampling rate R0 adopted in NFDM to ensure the accuracy of the NFT and inverse NFT (INFT) calculations, would cause the estimation accuracy of the traditional FFT-FOE method to decrease by R0 times. Moreover, CS-NFDM signals with higher baud rate require more subcarriers and then result in an oversampling factor greater than 16. This makes the traditional FFT-FOE method be ineffective to use the common training sequence (TS) overhead to meet the FOE error requirement of CS-NFDM system. Therefore, a modified FOE method based on FFT assisted by TS and autocorrelation has been proposed. The theoretical analysis and simulation results show that the proposed method is applicable to CS-NFDM system, no matter what modulation format is used. For 512 subcarriers, with a high rate of 70GBaud and the TS length of 8192, the proposed method can obtain a minimum FO estimation error about 0.1 MHz, which is better than the other two typical FFT-FOE and Schmidl & Cox methods. In addition, the proposed method can save at least 87.5% and 50% overhead. Thus, the proposed method has obvious improvement for CS-NFDM system with requiring high oversampling rate.

2.4-Tb/s/λ*km fundamental mode transmission over OM2 fiber employing Kramers-Kronig receiver.

We propose a digital-carrier Kramers-Kronig (DC-KK) scheme based high-speed multimode fiber short-reach optical interconnect system with fundamental mode transmission. After optimization of the parameters, including the roll-off factor of the root-raised-cosine (RRC) filter, and the guard interval (GI) between signal and carrier tone, as well as the carrier signal power ratio (CSPR), 200-Gb/s 32-quadrature amplitude modulation (32QAM) signal transmission over 12-km OM2 fiber has been experimentally demonstrated with a bit error ratio (BER) below the soft-decision forward error correction (SD-FEC) threshold of 4 × 10-2. To the best of our knowledge, this is the highest experimental record of single lambda bitrate-distance-product (SLBDP) achieved by direct-detection (DD)-based transmission over a standard multimode fiber (MMF). The proposed scheme has potential to improve the system performance without replacing massive deployed legacy MMFs for future large-capacity data center interconnects (DCIs).

Joint multi-parameter optical performance monitoring scheme based on trajectory information for a Stokes vector direct detection system.

In this study, we propose and verify a joint multi-parameter optical performance monitoring (OPM) scheme based on trajectory information for the Stokes vector direct detection (SVDD) system, for the first time, to the best of our knowledge. Here, the proposed scheme first performs quantification of the trajectory to construct trajectory information, which not only presents diversity of the received symbols in spatial dimension, but also records the jump pattern among symbols in time dimension. Subsequently, eigenanalysis is introduced to extract critical features hidden in trajectory information and simultaneously achieve the purpose of dimensionality reduction. The effectiveness of the scheme is verified through 14/28 GBaud SVDD binary phase shift keying/quadrature phase shift keying/-8 quadrature amplitude modulation (QAM)/-16QAM/-32QAM/-64QAM simulation systems. Under the scenario of joint modulation format (MF) identification and optical signal to noise ratio (OSNR) monitoring, the identification rates of all six kinds of MFs achieve 100% within their corresponding reasonable OSNR ranges. Besides that, the average mean absolute error (MAE) of the monitored OSNRs are obtained as 0.03 dB, 0.22 dB, 0.36 dB, 0.41 dB, 0.46 dB, and 0.49 dB for those six kinds of MFs, respectively. Under the scenario of multi-parameter OPM, SVDD-8QAM/-16QAM/-32QAM signals are 100% successfully identified when residual chromatic dispersion (RCD) is located in the ranges of 0-200 ps/nm, 0-190 ps/nm, and 0-160 ps/nm, respectively. The average MAE of OSNR monitoring and RCD estimation for these three commonly used MFs are 1.08 dB and 3.23 ps/nm, respectively. Moreover, the study also demonstrates the robustness for baud rates and a relatively simpler calculation complexity about the proposed OPM scheme.

Blind modulation format identification based on improved PSO clustering in a 2D Stokes plane.

Blind modulation format identification (MFI) is indispensable for correct signal demodulation and optical performance monitoring in future elastic optical networks (EON). Existing MFI schemes based on a clustering algorithm in Stokes space have gained good performance, while only limited types of modulation formats could be correctly identified, and the complexities are relatively high. In this work, we have proposed an MFI scheme with a low computational complexity, which combines an improved particle swarm optimization (I-PSO) clustering algorithm with a 2D Stokes plane. The main idea of I-PSO is to add a new field of view on each particle and limit each particle to only communicate with its neighbor particles, so as to realize the correct judgment of the number of multiple clusters (local extrema) on the density images of the s2-s3 plane. The effectiveness has been verified by 28 GBaud polarization division multiplexing (PDM)-BPSK/PDM-QPSK/PDM-8QAM/PDM-16QAM/PDM-32QAM/PDM-64QAM simulation EON systems and 28 GBaud PDM-QPSK/PDM-8QAM/PDM-16QAM/PDM-32QAM proof-of-concept transmission experiments. The results show that, using this MFI scheme, the minimum optical signal-to-noise ratio (OSNR) values to achieve 100% MFI success rate are all equal to or lower than those of the corresponding 7% forward error correction (FEC) thresholds. At the same time, the MFI scheme also obtains good tolerance to residual chromatic dispersion and differential group delay. Besides that, the proposed scheme achieves 100% MFI success rate within a maximum launch power range of -2∼+6 dBm. More importantly, its computational complexity can be denoted as O(N).

Blind and low-complexity modulation format identification scheme using principal component analysis of Stokes parameters for elastic optical networks.

We propose a blind and low-complexity modulation format identification (MFI) scheme for elastic optical networks (EONs). Since the square operation reduces half the number of the clusters in Stokes space, the scheme directly performs principal component analysis (PCA) on Stokes parameters after square operation. This greatly reduces the dimensionality of received signals from 3 × N to 3 × 3. Subsequently, three obtained principal components (PCs) are employed synthetically to identify the modulation formats. The effectiveness is first verified through 28 GBaud polarization division multiplexing (PDM)-BPSK/-QPSK/-8QAM/-16QAM/-32QAM/-64QAM simulation systems. Only using 2048 symbols, the required minimum optical signal-to-noise ratio (OSNR) values to achieve 100% MFI success rate are all equal to or lower than their corresponding 7% forward error correction (FEC) thresholds. Besides that, the scheme also obtains significant tolerances to residual chromatic dispersion (CD) and differential group delay (DGD). Finally, the proposed scheme is further verified by 20 GBaud PDM-QPSK/-16QAM/-32QAM long-haul transmission experiments. The results demonstrate that the scheme exhibits good resilience towards fiber nonlinear impairments. More importantly, compared with other four kinds of MFI schemes, the used symbol number to achieve 100% MFI success rate notably equals to at most 2/5 as that of other schemes, and its time complexity can be reduced to O(N).